Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

•P1 approximation of the radiative-conductive heat transfer model with Fresnel matching conditions are constructed.•The unique solvability of the complex heat transfer model in a multicomponent domain is proved.•Numerical experiments demonstrating the importance of accounting for the reflection and...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2018-04, Vol.57, p.290-298
Main Authors: Chebotarev, Alexander Yu, Grenkin, Gleb V., Kovtanyuk, Andrey E., Botkin, Nikolai D., Hoffmann, Karl-Heinz
Format: Article
Language:English
Subjects:
Approximation
Conductive heat transfer
Diffraction
Diffusion
Heat transfer
Mathematical analysis
Mathematical models
Numerical analysis
Radiative-conductive heat transfer
Reflection and refraction effects
Unique solvability
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Summary:•P1 approximation of the radiative-conductive heat transfer model with Fresnel matching conditions are constructed.•The unique solvability of the complex heat transfer model in a multicomponent domain is proved.•Numerical experiments demonstrating the importance of accounting for the reflection and refraction effects in modeling the radiative-conductive heat transfer are fulfilled. The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.10.004